import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import sklearn as sk
from sklearn.linear_model import LinearRegression
import statsmodels.api as sm
import statsmodels.formula.api as smf
from bokeh.plotting import figure, output_file, show
from bokeh.palettes import magma
from bokeh.models import ColumnDataSource
from plotnine import ggplot, aes, geom_point, theme_minimal, labs, theme, element_blank
from sklearn.experimental import enable_iterative_imputer
from sklearn.impute import IterativeImputer
import statsmodels.stats.diagnostic as ssd
import  statsmodels.stats.outliers_influence as oi
import statsmodels.stats.anova as av
import statsmodels.stats.oneway as ow
from statsmodels.tsa.stattools import adfuller
from statsmodels.stats.multicomp import pairwise_tukeyhsd

nhanes =pd.read_csv("clenning.ipynb (cnhanes).csv")

nhanes.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 10349 entries, 0 to 10348
Data columns (total 37 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   sampl       10349 non-null  float64
 1   strata      10349 non-null  float64
 2   location    10349 non-null  float64
 3   houssiz     10349 non-null  int64  
 4   age         10349 non-null  int64  
 5   height      10349 non-null  float64
 6   weight      10349 non-null  float64
 7   bpsystol    10349 non-null  int64  
 8   bpdiast     10349 non-null  int64  
 9   tcresult    10349 non-null  float64
 10  hdresult    10349 non-null  float64
 11  hgb         10349 non-null  float64
 12  hct         10349 non-null  float64
 13  tibc        10349 non-null  float64
 14  iron        10349 non-null  float64
 15  finalwgt    10349 non-null  float64
 16  leadwt      10349 non-null  float64
 17  corpuscl    10349 non-null  float64
 18  trnsfern    10349 non-null  float64
 19  albumin     10349 non-null  float64
 20  vitaminc    10349 non-null  float64
 21  zinc        10349 non-null  float64
 22  copper      10349 non-null  float64
 23  porphyrn    10349 non-null  float64
 24  hsizgp      10349 non-null  int64  
 25  bmi         10349 non-null  float64
 26  highbp      10349 non-null  int64  
 27  smsa_all    10349 non-null  int64  
 28  region_all  10349 non-null  int64  
 29  psu         10349 non-null  int64  
 30  sex         10349 non-null  int64  
 31  race        10349 non-null  int64  
 32  hlthstat    10349 non-null  object 
 33  heartatk    10349 non-null  int64  
 34  diabetes    10349 non-null  int64  
 35  sizplace    10349 non-null  object 
 36  rural       10349 non-null  int64  
dtypes: float64(21), int64(14), object(2)
memory usage: 2.9+ MB

nhanes.head()

nhanes.describe()

num_nhanes = nhanes.select_dtypes(include=['number'])

int_nhanes = nhanes.select_dtypes(include=['int'])

obj_nhanes = nhanes.select_dtypes(include=['object'])

# Set a color palette for better visualization
sns.set_palette("Set3")

# Assuming 'int_nhanes' is a list of column names and 'num_nhanes' is a DataFrame
for column in int_nhanes:
    plt.figure(figsize=(15, 8))
    
    # Skip certain columns
    if column in ['age', 'houssize', 'bpsystol']:
        continue

    # Plot the bar chart
    num_nhanes[column].value_counts().plot(kind='bar', color=sns.color_palette("Set3"), edgecolor='black')

    # Add labels and title
    plt.title(f'Distribution of {column}')
    plt.xlabel(f'{column}')
    plt.ylabel('Count')

    # Display the chart
    plt.show()

<Figure size 1500x800 with 0 Axes>

<Figure size 1500x800 with 0 Axes>

# Set a color palette for better visualization
sns.set_palette("pastel")

# Assuming 'obj_nhanes' is a DataFrame
for column in obj_nhanes:
    plt.figure(figsize=(12, 8))
    
    # Plot the bar chart
    obj_nhanes[column].value_counts().plot(kind='bar', color=sns.color_palette("pastel"), edgecolor='black')

    # Add labels and title
    plt.title(f'Distribution of {column}', fontsize=16)
    plt.xlabel(f'{column}', fontsize=14)
    plt.ylabel('Count', fontsize=14)

    # Add data labels on top of the bars
    for i, value in enumerate(obj_nhanes[column].value_counts()):
        plt.text(i, value + 0.1, str(value), ha='center', va='bottom', fontsize=12)

    # Display the chart
    plt.show()

# Set a custom color palette
custom_palette = sns.color_palette("coolwarm", as_cmap=True)

# Set up the matplotlib figure
plt.figure(figsize=(20, 15))

# Create a heatmap with correlation values annotated
heatmap = sns.heatmap(
    num_nhanes.corr(),
    annot=True,
    cmap=custom_palette,
    fmt=".2f",
    linewidths=0.5,
    annot_kws={"size": 12},
)

# Customize the aesthetics
heatmap.set_title("Correlation Heatmap", fontsize=18, fontweight='bold')

# Rotate the y-axis ticks for better readability
plt.yticks(rotation=0)

# Add color bar with labeled values
cbar = heatmap.collections[0].colorbar
cbar.ax.tick_params(labelsize=12)
cbar.set_label('Correlation Coefficient', fontsize=14)

# Add a shadow to the annotation for better contrast
for _, spine in heatmap.spines.items():
    spine.set_visible(True)
    spine.set_linewidth(1.5)
    spine.set_edgecolor("darkgray")

# Adjust layout for better spacing
plt.tight_layout()

# Show the heatmap
plt.show()

# Assuming num_nhanes is your DataFrame
# Make sure to replace it with your actual DataFrame

# Your plotting code with additional styling
fig, axes = plt.subplots(nrows=len(num_nhanes.columns), figsize=(15, 70), sharex=False)

# Use a professional Seaborn style
sns.set(style="whitegrid")

# Define a color palette for the box plots
custom_palette = sns.color_palette("husl")

for i, column in enumerate(num_nhanes.columns):
    sns.boxplot(x=num_nhanes[column], ax=axes[i], color=custom_palette[i % len(custom_palette)])
    axes[i].set_title(column, fontsize=16)
    axes[i].tick_params(labelsize=12)

# Adjust layout for better spacing
plt.tight_layout()

plt.suptitle("Box Plots of Numeric Variables", y=0.92, fontsize=20)
plt.show()

# Set Seaborn theme and color palette
sns.set_theme()
sns.set_palette("coolwarm")  # You can choose a different palette, for example, "coolwarm"

# Create a scatter matrix
scatter_matrix = pd.plotting.scatter_matrix(nhanes, figsize=(20, 20), diagonal="hist", alpha=0.7)

# Customize scatter matrix with Seaborn style
for ax in scatter_matrix.flatten():
    ax.xaxis.label.set_rotation(45)
    ax.yaxis.label.set_rotation(0)
    ax.yaxis.label.set_ha('right')

# Adjust layout
plt.tight_layout()

# Show the plot
plt.show()

# Set a custom color palette
custom_palette = sns.color_palette("husl", n_colors=len(nhanes.columns))

# Set up subplots
fig, axes = plt.subplots(nrows=len(nhanes.columns) // 2 + 1, ncols=2, figsize=(30, 70), sharex=False)

# Flatten the axes array to iterate over them
axes = axes.flatten()

# Iterate through each column and create a histogram
for i, column in enumerate(nhanes.columns):
    sns.histplot(nhanes[column], bins=20, ax=axes[i], color=custom_palette[i], kde=True)
    axes[i].set_title(f'Histogram for {column}', fontsize=16)
    axes[i].set_xlabel(column, fontsize=14)
    axes[i].set_ylabel('Frequency', fontsize=14)
    axes[i].grid(axis='y', linestyle='--', alpha=0.7)

# Remove empty subplots if there are an odd number of columns
if len(nhanes.columns) % 2 != 0:
    fig.delaxes(axes[-1])

# Adjust layout for better spacing
plt.tight_layout()

# Show the histograms
plt.show()

bmi_model = smf.ols('bmi~height+weight',data=nhanes).fit()

print(bmi_model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    bmi   R-squared:                       0.987
Model:                            OLS   Adj. R-squared:                  0.987
Method:                 Least Squares   F-statistic:                 3.910e+05
Date:                Tue, 02 Jan 2024   Prob (F-statistic):               0.00
Time:                        19:10:05   Log-Likelihood:                -8714.2
No. Observations:               10349   AIC:                         1.743e+04
Df Residuals:                   10346   BIC:                         1.746e+04
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept     52.0569      0.099    527.556      0.000      51.863      52.250
height        -0.3129      0.001   -480.782      0.000      -0.314      -0.312
weight         0.3608      0.000    881.698      0.000       0.360       0.362
==============================================================================
Omnibus:                     2044.475   Durbin-Watson:                   1.973
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            52372.699
Skew:                           0.289   Prob(JB):                         0.00
Kurtosis:                      14.006   Cond. No.                     3.27e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.27e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

residuals = bmi_model.resid
fitted = bmi_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence = oi.OLSInfluence(bmi_model).summary_frame()
influence

# Assuming 'bmi_model' is your regression model and 'influence' is the influence object

k = len(bmi_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence["student_resid"], color='blue', alpha=0.7, label='Residuals')
axs[0].axhline(y=3, color='red', linestyle='--', label='Threshold')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')
axs[0].legend(loc='upper right')
axs[0].grid(True, linestyle='--', alpha=0.5)

# Leverage Plot
axs[1].scatter(range(n), influence["hat_diag"], color='green', alpha=0.7, label='Leverage')
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--', label='Threshold')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')
axs[1].legend(loc='upper right')
axs[1].grid(True, linestyle='--', alpha=0.5)

# Cook's Distance Plot
axs[2].scatter(range(n), influence["cooks_d"], marker='o', color='red', label="Cook's Distance")
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--', label='Threshold 1')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--', label='Threshold 2')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")
axs[2].legend(loc='upper right')
axs[2].grid(True, linestyle='--', alpha=0.5)

plt.tight_layout()
plt.show()

bmi_hetro = ssd.het_breuschpagan(bmi_model.resid,bmi_model.model.exog)
bmi_hetro_test_statistic, bmi_hetro_p_value = bmi_hetro[:2]
bmi_hetro_test_statistic, bmi_hetro_p_value

(967.1836517532499, 9.522226953350605e-211)

bmi_model_t = smf.ols('np.log(bmi)~np.log(height)+np.log(weight)',data=nhanes).fit()
bmi_model_t.summary()

# Set seaborn style
sns.set(style="whitegrid")

# Create subplots
fig, axs = plt.subplots(2, 2, figsize=(20, 15))

# QQ Plot of Residuals
sm.qqplot(residuals, line='s', ax=axs[0, 0])
axs[0, 0].set_title('QQ Plot of Residuals')
axs[0, 0].grid(True, linestyle='--', alpha=0.5)

# Residuals vs Fitted Values
axs[0, 1].scatter(fitted, residuals, alpha=0.7, color='blue')
axs[0, 1].axhline(y=0, color='red', linestyle='--')
axs[0, 1].set_xlabel('Fitted Values')
axs[0, 1].set_ylabel('Residuals')
axs[0, 1].set_title('Residuals vs Fitted Values')
axs[0, 1].grid(True, linestyle='--', alpha=0.5)

# Histogram of Residuals
axs[1, 0].hist(residuals, bins=15, edgecolor='black', color='green', alpha=0.7)
axs[1, 0].set_title('Histogram of Residuals')
axs[1, 0].set_xlabel('Residuals')
axs[1, 0].set_ylabel('Frequency')
axs[1, 0].grid(True, linestyle='--', alpha=0.5)

# Boxplot of Residuals
sns.boxplot(x=residuals, ax=axs[1, 1], color='orange')
axs[1, 1].set_title('Boxplot of Residuals')
axs[1, 1].set_xlabel('Residuals')
axs[1, 1].grid(True, linestyle='--', alpha=0.5)

# Adjust layout
plt.tight_layout()
plt.show()

influence_1 = oi.OLSInfluence(bmi_model_t).summary_frame()
influence_1

k = len(bmi_model_t.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_1["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_1["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_1["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

bmi_hetro_t = ssd.het_breuschpagan(bmi_model_t.resid,bmi_model_t.model.exog)

bmi_hetro_t_test_statistic, bmi_hetro_p_value = bmi_hetro_t[:2]
bmi_hetro_t_test_statistic, bmi_hetro_p_value

(101.8565950128779, 7.622921021692244e-23)

waight =1/(bmi_model.resid**2)

bmi_model_weight = smf.wls('bmi~height+weight',data=nhanes,weights=waight).fit()

bmi_model_weight.summary()

residuals = bmi_model_weight.resid
fitted = bmi_model_weight.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_2 = oi.OLSInfluence(bmi_model_weight).summary_frame()
influence_2

k = len(bmi_model_weight.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_2["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_2["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_2["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

bmi_hetro_weight = ssd.het_breuschpagan(bmi_model_weight.resid,bmi_model_weight.model.exog)
bmi_hetro_weight_test_statistic, bmi_hetro_weight_p_value = bmi_hetro_weight[:2]
bmi_hetro_weight_test_statistic, bmi_hetro_weight_p_value

(967.5655281012215, 7.867108374853343e-211)

bmi_model_weight_t = smf.wls('np.log(bmi)~np.log(height)+np.log(weight)',data=nhanes,weights=waight).fit()

bmi_model_weight_t.summary()

residuals = bmi_model_weight_t.resid
fitted = bmi_model_weight_t.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_3 = oi.OLSInfluence(bmi_model_weight_t).summary_frame()
influence_3

k = len(bmi_model_weight_t.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_3["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_3["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_3["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

bmi_hetro_weight_t = ssd.het_breuschpagan(bmi_model_weight_t.resid,bmi_model_weight_t.model.exog)
bmi_hetro_weight_t_test_statistic, bmi_hetro_weight_t_p_value = bmi_hetro_weight_t[:2]
bmi_hetro_weight_t_test_statistic, bmi_hetro_weight_t_p_value

(468.3283891062324, 2.012715755520839e-102)

#heart_model = smf.ols('(highbp)~bpdiast+bpsystol',data=nhanes).fit()
highbp_model = smf.logit('(highbp)~bpdiast+bpsystol',data=nhanes).fit()

Optimization terminated successfully.
         Current function value: 0.165689
         Iterations 10

print(highbp_model.summary())

                           Logit Regression Results                           
==============================================================================
Dep. Variable:                 highbp   No. Observations:                10349
Model:                          Logit   Df Residuals:                    10346
Method:                           MLE   Df Model:                            2
Date:                Tue, 02 Jan 2024   Pseudo R-squ.:                  0.7568
Time:                        19:12:23   Log-Likelihood:                -1714.7
converged:                       True   LL-Null:                       -7049.7
Covariance Type:            nonrobust   LLR p-value:                     0.000
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    -49.6261      1.249    -39.741      0.000     -52.074     -47.179
bpdiast        0.2504      0.008     32.661      0.000       0.235       0.265
bpsystol       0.2176      0.006     36.483      0.000       0.206       0.229
==============================================================================

Possibly complete quasi-separation: A fraction 0.22 of observations can be
perfectly predicted. This might indicate that there is complete
quasi-separation. In this case some parameters will not be identified.

bpsystol_model = smf.ols('(bpsystol)~age+vitaminc+zinc',data=nhanes).fit()

bpsystol_model.summary()

residuals = bpsystol_model.resid
fitted = bpsystol_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_4 = oi.OLSInfluence(bpsystol_model).summary_frame()
influence_4

k = len(bpsystol_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_4["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_4["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_4["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

bpsystol_hetro = ssd.het_breuschpagan(bpsystol_model.resid,bpsystol_model.model.exog)
bpsystol_hetro_test_statistic, bpsystol_hetro_p_value = bpsystol_hetro[:2]
bpsystol_hetro_test_statistic, bpsystol_hetro_p_value

(331.23772728871336, 1.7216965915181788e-71)

waight =1/(bpsystol_model.resid**2)

w_bpsystol_model=smf.wls('np.log(bpsystol)~np.log(age)+np.log(vitaminc)+np.log(zinc)',data=nhanes,weights=waight).fit()

print(w_bpsystol_model.summary())

                            WLS Regression Results                            
==============================================================================
Dep. Variable:       np.log(bpsystol)   R-squared:                       0.997
Model:                            WLS   Adj. R-squared:                  0.997
Method:                 Least Squares   F-statistic:                 1.060e+06
Date:                Tue, 02 Jan 2024   Prob (F-statistic):               0.00
Time:                        19:12:59   Log-Likelihood:                 1758.7
No. Observations:               10349   AIC:                            -3509.
Df Residuals:                   10345   BIC:                            -3480.
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
====================================================================================
                       coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------
Intercept            3.9423      0.002   1883.143      0.000       3.938       3.946
np.log(age)          0.2285      0.000   1052.018      0.000       0.228       0.229
np.log(vitaminc)    -0.0091      0.000    -79.817      0.000      -0.009      -0.009
np.log(zinc)         0.0131      0.000     28.470      0.000       0.012       0.014
==============================================================================
Omnibus:                    12268.391   Durbin-Watson:                   1.991
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         86513464.009
Skew:                           4.909   Prob(JB):                         0.00
Kurtosis:                     450.810   Cond. No.                     2.05e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.05e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

residuals = w_bpsystol_model.resid
fitted = w_bpsystol_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_5 = oi.OLSInfluence(w_bpsystol_model).summary_frame()
influence_5

k = len(w_bpsystol_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_5["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_5["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_5["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

w_bpsystol_hetro = ssd.het_breuschpagan(w_bpsystol_model.resid,w_bpsystol_model.model.exog)
w_bpsystol_hetro_test_statistic, w_bpsystol_hetro_p_value = w_bpsystol_hetro[:2]
w_bpsystol_hetro_test_statistic, w_bpsystol_hetro_p_value

(113.76338285050466, 1.699436814369022e-24)

hct_model = smf.ols('(tcresult)~weight+age+sex+hdresult',data=nhanes).fit()

print(hct_model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               tcresult   R-squared:                       0.176
Model:                            OLS   Adj. R-squared:                  0.176
Method:                 Least Squares   F-statistic:                     553.2
Date:                Tue, 02 Jan 2024   Prob (F-statistic):               0.00
Time:                        19:13:42   Log-Likelihood:                -54038.
No. Observations:               10349   AIC:                         1.081e+05
Df Residuals:                   10344   BIC:                         1.081e+05
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    130.4219      3.379     38.599      0.000     123.799     137.045
weight         0.3408      0.032     10.670      0.000       0.278       0.403
age            1.1178      0.026     43.582      0.000       1.068       1.168
sex           -9.8938      0.973    -10.170      0.000     -11.801      -7.987
hdresult       0.2877      0.036      8.089      0.000       0.218       0.357
==============================================================================
Omnibus:                     2341.500   Durbin-Watson:                   1.964
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            13428.607
Skew:                           0.964   Prob(JB):                         0.00
Kurtosis:                       8.237   Cond. No.                         770.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

residuals = hct_model.resid
fitted = hct_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_6 = oi.OLSInfluence(hct_model).summary_frame()
influence_6

k = len(hct_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_6["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_6["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_6["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

hct_hetro = ssd.het_breuschpagan(hct_model.resid,hct_model.model.exog)
hct_hetro_test_statistic, hct_hetro_p_value = hct_hetro[:2]
hct_hetro_test_statistic, hct_hetro_p_value

(45.2018457287695, 3.6097148786843032e-09)

hct_model_t = smf.ols('np.log(tcresult)~weight+age+sex+hdresult',data=nhanes).fit()

print(hct_model_t.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       np.log(tcresult)   R-squared:                       0.191
Model:                            OLS   Adj. R-squared:                  0.191
Method:                 Least Squares   F-statistic:                     610.1
Date:                Tue, 02 Jan 2024   Prob (F-statistic):               0.00
Time:                        19:14:20   Log-Likelihood:                 1875.4
No. Observations:               10349   AIC:                            -3741.
Df Residuals:                   10344   BIC:                            -3705.
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept      4.9301      0.015    323.962      0.000       4.900       4.960
weight         0.0017      0.000     11.717      0.000       0.001       0.002
age            0.0053      0.000     45.691      0.000       0.005       0.006
sex           -0.0420      0.004     -9.580      0.000      -0.051      -0.033
hdresult       0.0015      0.000      9.501      0.000       0.001       0.002
==============================================================================
Omnibus:                      121.094   Durbin-Watson:                   1.958
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              213.912
Skew:                          -0.002   Prob(JB):                     3.54e-47
Kurtosis:                       3.704   Cond. No.                         770.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

residuals = hct_model_t.resid
fitted = hct_model_t.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_7 = oi.OLSInfluence(hct_model_t).summary_frame()
influence_7

k = len(hct_model_t.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_7["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_7["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_7["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

hct_hetro_t = ssd.het_breuschpagan(hct_model_t.resid,hct_model_t.model.exog)
hct_hetro_t_test_statistic, hct_hetro_t_p_value = hct_hetro_t[:2]
print(hct_hetro_t_test_statistic, hct_hetro_t_p_value)

51.583116803179465 1.6860345998642798e-10

weight =1/(bpsystol_model.resid**2)

w_hct_model=smf.wls('(tcresult)~weight+age+sex+hdresult',data=nhanes,weights=waight).fit()

w_hct_model.summary()

residuals = w_hct_model.resid
fitted = w_hct_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_8 = oi.OLSInfluence(w_hct_model).summary_frame()
influence_8

k = len(w_hct_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_8["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_8["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_8["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

w_hct_hetro = ssd.het_breuschpagan(w_hct_model.resid,w_hct_model.model.exog)
w_hct_hetro_test_statistic, w_hct_hetro_p_value = w_hct_hetro[:2]
w_hct_hetro_test_statistic, w_hct_hetro_p_value

(363.19206191897774, 2.4850615620944477e-77)

w_hct_model_t=smf.wls('np.log(tcresult)~weight+age+sex+hdresult',data=nhanes,weights=waight).fit()

print(w_hct_model_t.summary())

                            WLS Regression Results                            
==============================================================================
Dep. Variable:       np.log(tcresult)   R-squared:                       0.560
Model:                            WLS   Adj. R-squared:                  0.559
Method:                 Least Squares   F-statistic:                     3286.
Date:                Tue, 02 Jan 2024   Prob (F-statistic):               0.00
Time:                        19:15:38   Log-Likelihood:                -27326.
No. Observations:               10349   AIC:                         5.466e+04
Df Residuals:                   10344   BIC:                         5.470e+04
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept      5.4629      0.008    658.489      0.000       5.447       5.479
weight        -0.0029      0.000    -20.318      0.000      -0.003      -0.003
age            0.0073    9.9e-05     73.766      0.000       0.007       0.007
sex            0.0563      0.004     13.570      0.000       0.048       0.064
hdresult      -0.0032      0.000    -18.001      0.000      -0.004      -0.003
==============================================================================
Omnibus:                    20901.237   Durbin-Watson:                   1.978
Prob(Omnibus):                  0.000   Jarque-Bera (JB):        199376382.225
Skew:                         -16.101   Prob(JB):                         0.00
Kurtosis:                     682.213   Cond. No.                     7.39e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 7.39e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

residuals = w_hct_model_t.resid
fitted = w_hct_model_t.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_9 = oi.OLSInfluence(w_hct_model_t).summary_frame()
influence_9

k = len(w_hct_model_t.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_9["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_9["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_9["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

w_hct_hetro_t = ssd.het_breuschpagan(w_hct_model_t.resid,w_hct_model_t.model.exog)
w_hct_hetro_t_test_statistic, w_hct_hetro_t_p_value = w_hct_hetro_t[:2]
w_hct_hetro_t_test_statistic, w_hct_hetro_t_p_value

(561.6795982616044, 3.0396757538430395e-120)

diabetes_model = smf.logit('(heartatk)~age+sex+weight',data=nhanes).fit()

Optimization terminated successfully.
         Current function value: 0.156972
         Iterations 9

print(diabetes_model.summary())

                           Logit Regression Results                           
==============================================================================
Dep. Variable:               heartatk   No. Observations:                10349
Model:                          Logit   Df Residuals:                    10345
Method:                           MLE   Df Model:                            3
Date:                Tue, 02 Jan 2024   Pseudo R-squ.:                  0.1585
Time:                        19:16:18   Log-Likelihood:                -1624.5
converged:                       True   LL-Null:                       -1930.6
Covariance Type:            nonrobust   LLR p-value:                2.314e-132
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept     -8.9833      0.422    -21.294      0.000      -9.810      -8.156
age            0.0866      0.005     17.536      0.000       0.077       0.096
sex            0.8422      0.107      7.904      0.000       0.633       1.051
weight         0.0075      0.003      2.163      0.031       0.001       0.014
==============================================================================

a_bmi_model = smf.ols('(bmi)~hlthstat',data=nhanes).fit()
print(a_bmi_model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    bmi   R-squared:                       0.021
Model:                            OLS   Adj. R-squared:                  0.021
Method:                 Least Squares   F-statistic:                     45.14
Date:                Tue, 02 Jan 2024   Prob (F-statistic):           2.92e-46
Time:                        19:16:18   Log-Likelihood:                -31052.
No. Observations:               10349   AIC:                         6.212e+04
Df Residuals:                   10343   BIC:                         6.216e+04
Df Model:                           5                                         
Covariance Type:            nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
Intercept                24.7449      1.300     19.036      0.000      22.197      27.293
hlthstat[T.Excellent]    -0.1844      1.304     -0.141      0.888      -2.740       2.371
hlthstat[T.Fair]          1.8485      1.305      1.416      0.157      -0.710       4.407
hlthstat[T.Good]          1.0648      1.303      0.817      0.414      -1.489       3.619
hlthstat[T.Poor]          1.7372      1.312      1.324      0.186      -0.835       4.310
hlthstat[T.Very good]     0.4510      1.303      0.346      0.729      -2.104       3.006
==============================================================================
Omnibus:                     2142.582   Durbin-Watson:                   2.007
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5451.507
Skew:                           1.132   Prob(JB):                         0.00
Kurtosis:                       5.742   Cond. No.                         74.0
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

av.anova_lm(a_bmi_model)

bmi_model_a_h = smf.ols('(bmi)~hlthstat+weight',data=nhanes).fit()
print(bmi_model_a_h.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    bmi   R-squared:                       0.708
Model:                            OLS   Adj. R-squared:                  0.708
Method:                 Least Squares   F-statistic:                     4174.
Date:                Tue, 02 Jan 2024   Prob (F-statistic):               0.00
Time:                        19:16:18   Log-Likelihood:                -24799.
No. Observations:               10349   AIC:                         4.961e+04
Df Residuals:                   10342   BIC:                         4.966e+04
Df Model:                           6                                         
Covariance Type:            nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
Intercept                 6.3204      0.720      8.776      0.000       4.909       7.732
hlthstat[T.Excellent]    -0.6292      0.712     -0.883      0.377      -2.026       0.767
hlthstat[T.Fair]          0.9241      0.713      1.295      0.195      -0.474       2.323
hlthstat[T.Good]          0.4007      0.712      0.563      0.574      -0.995       1.797
hlthstat[T.Poor]          0.7525      0.717      1.049      0.294      -0.653       2.158
hlthstat[T.Very good]    -0.1425      0.712     -0.200      0.841      -1.539       1.254
weight                    0.2654      0.002    155.842      0.000       0.262       0.269
==============================================================================
Omnibus:                      969.723   Durbin-Watson:                   1.965
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1593.163
Skew:                           0.684   Prob(JB):                         0.00
Kurtosis:                       4.350   Cond. No.                     4.90e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 4.9e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

av.anova_lm(bmi_model_a_h)

	sampl	strata	location	houssiz	age	height	weight	bpsystol	bpdiast	tcresult	...	bmi	highbp	smsa_all	region_all	psu	sex	race	heartatk	diabetes	rural
count	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	...	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000
mean	33623.454054	16.664605	33.063388	2.943376	47.581795	167.652605	71.899767	130.886656	81.716301	217.676974	...	25.537892	0.422843	2.200792	2.581119	0.481882	0.474925	0.143589	0.045995	0.048217	0.367378
std	18412.384315	9.496886	18.412662	1.695022	17.215566	9.655687	15.357050	23.332026	12.927943	49.384976	...	4.915345	0.494035	0.818039	1.075303	0.499696	0.499395	0.402042	0.209484	0.214235	0.482114
min	1400.000000	1.000000	1.000000	1.000000	20.000000	135.500000	30.840000	65.000000	35.000000	80.000000	...	12.385596	0.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
25%	17402.000000	8.000000	17.000000	2.000000	31.000000	160.500000	60.669998	114.000000	70.000000	183.000000	...	22.142040	0.000000	1.000000	2.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
50%	34678.000000	16.000000	34.000000	2.000000	49.000000	167.296997	70.419998	128.000000	80.000000	213.000000	...	24.818115	0.000000	2.000000	3.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
75%	49435.000000	25.000000	49.000000	4.000000	63.000000	174.598007	81.190002	142.000000	90.000000	247.000000	...	28.026737	1.000000	3.000000	4.000000	1.000000	1.000000	0.000000	0.000000	0.000000	1.000000
max	64709.000000	32.000000	64.000000	14.000000	74.000000	200.000000	175.880005	300.000000	150.000000	828.000000	...	61.129696	1.000000	3.000000	4.000000	1.000000	1.000000	2.000000	1.000000	1.000000	1.000000

	dfb_Intercept	dfb_height	dfb_weight	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	-0.008283	0.010682	-0.010098	7.748955e-05	0.943259	0.000261	0.015247	0.943254	0.015247
1	-0.023915	0.016863	0.014474	4.102288e-04	-1.730113	0.000411	-0.035081	-1.730280	-0.035085
2	0.000009	-0.000006	-0.000003	2.110994e-10	0.002380	0.000112	0.000025	0.002380	0.000025
3	0.008334	-0.011456	0.016078	1.148557e-04	0.835849	0.000493	0.018563	0.835836	0.018562
4	0.001095	-0.001108	0.000772	1.495494e-06	0.181468	0.000136	0.002118	0.181460	0.002118
...	...	...	...	...	...	...	...	...	...
10344	-0.000036	0.000221	-0.000596	2.212620e-07	0.056057	0.000211	0.000815	0.056055	0.000815
10345	0.028452	-0.040529	0.058516	1.334231e-03	1.966865	0.001034	0.063267	1.967138	0.063276
10346	0.004839	-0.007037	0.010903	5.120372e-05	0.560555	0.000489	0.012394	0.560536	0.012394
10347	-0.000386	0.001090	-0.002407	3.033011e-06	0.184780	0.000266	0.003016	0.184771	0.003016
10348	-0.008434	0.011523	-0.012597	9.834520e-05	1.001989	0.000294	0.017177	1.001990	0.017177

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	9.2103	2.19e-08	4.21e+08	0.000	9.210	9.210
np.log(height)	-2.0000	4.7e-09	-4.25e+08	0.000	-2.000	-2.000
np.log(weight)	1.0000	1.29e-09	7.73e+08	0.000	1.000	1.000

	dfb_Intercept	dfb_np.log(height)	dfb_np.log(weight)	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	0.002652	-0.003082	0.002825	6.226806e-06	-0.268326	0.000259	-0.004322	-0.268314	-0.004322
1	-0.010212	0.007198	0.008747	1.064247e-04	-0.825596	0.000468	-0.017868	-0.825583	-0.017868
2	-0.001732	0.001459	0.000269	1.068729e-05	-0.544204	0.000108	-0.005662	-0.544185	-0.005662
3	-0.022847	0.029996	-0.041371	7.660943e-04	-2.202312	0.000474	-0.047940	-2.202722	-0.047949
4	-0.004691	0.005173	-0.004326	3.035029e-05	-0.789178	0.000146	-0.009542	-0.789163	-0.009542
...	...	...	...	...	...	...	...	...	...
10344	0.002446	-0.005091	0.012103	8.544582e-05	-1.060958	0.000228	-0.016011	-1.060965	-0.016011
10345	-0.010889	0.014319	-0.019689	1.555758e-04	-0.730888	0.000873	-0.021604	-0.730872	-0.021603
10346	-0.015048	0.020696	-0.031458	4.322525e-04	-1.680699	0.000459	-0.036011	-1.680847	-0.036014
10347	-0.004760	0.008281	-0.016836	1.379631e-04	1.161470	0.000307	0.020344	1.161489	0.020345
10348	-0.000339	0.000412	-0.000445	1.215124e-07	0.034616	0.000304	0.000604	0.034615	0.000604

	dfb_Intercept	dfb_height	dfb_weight	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	-3.820567	3.180320	0.481855	1.788729e-09	0.529801	1.911793e-08	0.000073	0.943060	0.000130
1	-6.496168	4.154956	3.894840	2.974639e-09	-0.971579	9.453641e-09	-0.000094	-1.729614	-0.000168
2	-2.401447	1.495159	1.883829	4.891402e-13	0.001336	8.222567e-07	0.000001	0.002378	0.000002
3	-0.976751	-0.310018	4.117442	3.376737e-09	0.469309	4.599395e-08	0.000101	0.835376	0.000179
4	-2.215613	1.321431	1.991508	8.021278e-11	0.101905	2.317248e-08	0.000016	0.181387	0.000028
...	...	...	...	...	...	...	...	...	...
10344	-2.409211	1.531018	1.801557	6.953998e-11	0.031534	2.097983e-07	0.000014	0.056129	0.000026
10345	2.465891	-4.893396	10.011843	1.840687e-08	1.104185	4.529162e-08	0.000235	1.965763	0.000418
10346	-1.574822	0.386636	3.398654	2.260447e-09	0.314675	6.848412e-08	0.000082	0.560116	0.000147
10347	-2.469097	1.668005	1.549988	3.350159e-10	0.103847	9.319701e-08	0.000032	0.184842	0.000056
10348	-3.846511	3.312785	0.134748	2.239412e-09	0.562804	2.121004e-08	0.000082	1.001812	0.000146

intro¶

Objectives¶

questions¶

Analysis¶

descrptive analysis¶

exploratory analysis¶

bmi model¶

transformation¶

Weight least squaren bmi model¶

transformation¶

logestic highbp model¶

bpsystol_model¶

weight¶

hct_model¶

transformation¶

weight¶

wtransformation¶

diabetes_logistic_model¶

ANOVA¶

	sampl	strata	location	houssiz	age	height	weight	bpsystol	bpdiast	tcresult	...	smsa_all	region_all	sex	race	hlthstat	diabetes	sizplace
0	1400.0	1.0	1.0	4	54	174.598007	62.480000	106	80	226.0	...	2	3	1	0	Very good	0	Urbanized area; 1,000,000–2,999,999
1	1401.0	1.0	1.0	6	41	152.296997	48.759998	108	66	179.0	...	2	3	0	0	Very good	0	Urbanized area; 1,000,000–2,999,999
2	1402.0	1.0	1.0	6	21	164.098007	67.250000	98	66	137.0	...	1	3	0	2	Good	0	Urbanized area; 1,000,000–2,999,999
3	1404.0	1.0	1.0	9	63	162.598007	94.459999	180	80	189.0	...	2	3	0	0	Fair	1	Urbanized area; 1,000,000–2,999,999
4	1405.0	1.0	1.0	3	64	163.098007	74.279999	120	76	311.0	...	1	3	0	0	Very good	0	Urbanized area; 1,000,000–2,999,999

Dep. Variable:	np.log(bmi)	R-squared:	1.000
Model:	OLS	Adj. R-squared:	1.000
Method:	Least Squares	F-statistic:	2.997e+17
Date:	Tue, 02 Jan 2024	Prob (F-statistic):	0.00
Time:	19:10:38	Log-Likelihood:	1.6692e+05
No. Observations:	10349	AIC:	-3.338e+05
Df Residuals:	10346	BIC:	-3.338e+05
Df Model:	2
Covariance Type:	nonrobust

Omnibus:	1915.638	Durbin-Watson:	2.006
Prob(Omnibus):	0.000	Jarque-Bera (JB):	397.592
Skew:	-0.008	Prob(JB):	4.61e-87
Kurtosis:	2.040	Cond. No.	640.

Omnibus:	36139.684	Durbin-Watson:	1.990
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1722.848
Skew:	-0.154	Prob(JB):	0.00
Kurtosis:	1.025	Cond. No.	5.92e+03

Omnibus:	14525.745	Durbin-Watson:	1.979
Prob(Omnibus):	0.000	Jarque-Bera (JB):	701920793.966
Skew:	6.556	Prob(JB):	0.00
Kurtosis:	1278.785	Cond. No.	1.16e+03

	dfb_Intercept	dfb_np.log(height)	dfb_np.log(weight)	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	-1407.645095	-1608.169557	11310.367961	6.257807e-14	0.003316	1.707160e-08	4.332831e-07	0.576415	0.000075
1	-1409.929118	-1606.493633	11311.621433	7.011945e-14	0.004243	1.168623e-08	4.586484e-07	0.737490	0.000080
2	-1408.424602	-1607.425725	11310.093143	9.904573e-14	-0.000609	8.003879e-07	-5.451029e-07	-0.105909	-0.000095
3	-1412.415500	-1602.995810	11306.112146	3.530862e-12	-0.017937	3.292203e-08	-3.254626e-06	-3.118591	-0.000566
4	-1408.962658	-1606.828458	11309.557705	1.402281e-13	-0.004336	2.237797e-08	-6.486018e-07	-0.753668	-0.000113
...	...	...	...	...	...	...	...	...	...
10344	-1407.752681	-1608.588153	11312.385671	2.359904e-14	0.000569	2.186060e-07	2.660773e-07	0.098923	0.000046
10345	-1410.037000	-1605.288323	11307.121688	1.488670e-12	-0.012496	2.860106e-08	-2.113294e-06	-2.172096	-0.000367
10346	-1410.918013	-1604.397408	11306.544982	3.654452e-12	-0.015168	4.765318e-08	-3.311096e-06	-2.636841	-0.000576
10347	-1409.024000	-1606.363851	11308.010429	7.061954e-12	0.014485	1.009801e-07	4.602810e-06	2.517865	0.000800
10348	-1408.161659	-1607.578389	11309.820971	2.510902e-13	0.006188	1.967393e-08	8.679116e-07	1.075546	0.000151

Omnibus:	1508.834	Durbin-Watson:	1.882
Prob(Omnibus):	0.000	Jarque-Bera (JB):	3274.172
Skew:	0.871	Prob(JB):	0.00
Kurtosis:	5.136	Cond. No.	741.

	dfb_Intercept	dfb_age	dfb_vitaminc	dfb_zinc	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	0.013587	-0.009267	0.016638	-0.019103	0.000226	-1.502539	0.000400	-0.030057	-1.502630	-0.030059
1	0.011816	0.001852	-0.003179	-0.015258	0.000082	-0.890232	0.000415	-0.018134	-0.890223	-0.018134
2	0.001965	0.010480	-0.004517	-0.006806	0.000059	-0.721430	0.000453	-0.015355	-0.721413	-0.015355
3	-0.033169	0.020354	0.001172	0.032789	0.000428	1.914864	0.000467	0.041399	1.915111	0.041405
4	0.012379	-0.010404	-0.004000	-0.010454	0.000080	-1.033530	0.000300	-0.017911	-1.033533	-0.017911
...	...	...	...	...	...	...	...	...	...	...
10344	-0.006310	0.009234	0.002159	0.000657	0.000066	-1.318416	0.000151	-0.016210	-1.318463	-0.016210
10345	-0.018704	-0.009213	0.005780	0.026758	0.000270	1.426432	0.000531	0.032881	1.426503	0.032883
10346	0.000960	-0.002034	0.000784	-0.000870	0.000003	-0.264971	0.000167	-0.003423	-0.264959	-0.003423
10347	-0.013480	0.008824	-0.000092	0.010900	0.000057	-0.719964	0.000439	-0.015080	-0.719947	-0.015079
10348	0.004149	0.006643	0.009348	-0.012063	0.000102	-0.954993	0.000447	-0.020188	-0.954989	-0.020188

	dfb_Intercept	dfb_np.log(age)	dfb_np.log(vitaminc)	dfb_np.log(zinc)	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	-8.858410	16.715465	5.017260	2.873971	0.000063	-12.749687	1.544943e-06	-0.015847	-1.731563	-0.002152
1	-8.879692	16.741544	4.942133	2.885236	0.000033	-8.289780	1.941904e-06	-0.011552	-1.125766	-0.001569
2	-8.918454	16.772137	4.940549	2.912788	0.000067	-5.463604	8.913152e-06	-0.016312	-0.741949	-0.002215
3	-9.018601	16.783274	4.972426	3.013385	0.000017	11.956310	4.875582e-07	0.008349	1.623841	0.001134
4	-8.891533	16.719513	4.941996	2.906276	0.000010	-8.002198	5.953609e-07	-0.006174	-1.086700	-0.000838
...	...	...	...	...	...	...	...	...	...	...
10344	-8.933459	16.763099	4.954153	2.931074	0.000031	-12.272100	8.212140e-07	-0.011121	-1.666701	-0.001510
10345	-8.984717	16.723911	4.978643	3.002281	0.000058	10.267174	2.217606e-06	0.015290	1.394359	0.002076
10346	-8.922247	16.737096	4.956896	2.931447	0.000002	-1.960406	1.766388e-06	-0.002605	-0.266212	-0.000354
10347	-8.973436	16.763943	4.950493	2.972273	0.000052	-6.013828	5.785778e-06	-0.014465	-0.816672	-0.001964
10348	-8.892756	16.758000	4.996542	2.892280	0.000059	-8.422671	3.347058e-06	-0.015409	-1.143825	-0.002093

	dfb_Intercept	dfb_weight	dfb_age	dfb_sex	dfb_hdresult	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	0.000851	-0.002113	0.000863	0.002828	0.000289	0.000003	0.206135	0.000338	0.003792	0.206126	0.003792
1	-0.007460	0.007894	0.002211	0.002760	0.000107	0.000031	-0.673656	0.000343	-0.012486	-0.673638	-0.012486
2	-0.005642	-0.002731	0.019411	0.010422	-0.004885	0.000137	-1.256020	0.000434	-0.026162	-1.256055	-0.026163
3	0.010737	-0.021636	-0.010060	0.020537	0.006109	0.000202	-1.249936	0.000646	-0.031771	-1.249970	-0.031772
4	-0.002996	0.006551	0.014264	-0.016867	-0.004419	0.000147	1.555982	0.000304	0.027124	1.556089	0.027126
...	...	...	...	...	...	...	...	...	...	...	...
10344	-0.004314	0.002894	0.002918	0.002728	0.000722	0.000010	-0.423845	0.000283	-0.007137	-0.423828	-0.007137
10345	-0.020276	0.059574	-0.021047	-0.043642	-0.007308	0.001055	2.201124	0.001087	0.072622	2.201533	0.072636
10346	0.005650	-0.015917	-0.005854	0.015929	0.007540	0.000117	-0.910113	0.000703	-0.024143	-0.910106	-0.024143
10347	-0.004586	0.003638	0.005141	0.002448	-0.001361	0.000018	-0.493693	0.000374	-0.009552	-0.493675	-0.009552
10348	-0.006684	0.008135	0.006144	-0.009881	-0.001152	0.000043	-0.693055	0.000450	-0.014709	-0.693038	-0.014709

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	101.9046	1.489	68.439	0.000	98.986	104.823
age	0.6598	0.012	55.977	0.000	0.637	0.683
vitaminc	-2.4051	0.353	-6.816	0.000	-3.097	-1.713
zinc	0.0009	0.015	0.059	0.953	-0.028	0.029

	dfb_Intercept	dfb_weight	dfb_age	dfb_sex	dfb_hdresult	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	0.001329	-0.003300	0.001347	0.004416	0.000451	0.000007	0.321937	0.000338	0.005922	0.321923	0.005922
1	-0.007001	0.007409	0.002075	0.002590	0.000100	0.000027	-0.632279	0.000343	-0.011719	-0.632261	-0.011719
2	-0.007153	-0.003463	0.024612	0.013215	-0.006194	0.000220	-1.592499	0.000434	-0.033171	-1.592617	-0.033174
3	0.010360	-0.020877	-0.009708	0.019817	0.005895	0.000188	-1.206109	0.000646	-0.030657	-1.206135	-0.030657
4	-0.002602	0.005689	0.012386	-0.014646	-0.003837	0.000111	1.351162	0.000304	0.023553	1.351216	0.023554
...	...	...	...	...	...	...	...	...	...	...	...
10344	-0.003534	0.002371	0.002390	0.002235	0.000591	0.000007	-0.347238	0.000283	-0.005847	-0.347223	-0.005847
10345	-0.018416	0.054109	-0.019116	-0.039638	-0.006638	0.000870	1.999271	0.001087	0.065962	1.999560	0.065972
10346	0.005113	-0.014404	-0.005298	0.014415	0.006823	0.000095	-0.823637	0.000703	-0.021849	-0.823625	-0.021848
10347	-0.004281	0.003396	0.004799	0.002285	-0.001270	0.000016	-0.460867	0.000374	-0.008917	-0.460849	-0.008917
10348	-0.007663	0.009326	0.007044	-0.011328	-0.001320	0.000057	-0.794543	0.000450	-0.016863	-0.794528	-0.016863

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	223.1733	1.735	128.622	0.000	219.772	226.574
weight	-0.5026	0.030	-16.690	0.000	-0.562	-0.444
age	1.6590	0.021	80.121	0.000	1.618	1.700
sex	11.2799	0.868	12.997	0.000	9.579	12.981
hdresult	-0.6615	0.037	-17.708	0.000	-0.735	-0.588

	dfb_Intercept	dfb_weight	dfb_age	dfb_sex	dfb_hdresult	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	84.351163	-44.195624	41.241521	38.501180	-40.093233	8.459852e-08	-0.468091	0.000002	-0.000650	-0.738609	-0.001026
1	84.327301	-44.179755	41.244977	38.501825	-40.094304	1.015453e-06	-0.708792	0.000010	-0.002253	-1.118436	-0.003556
2	84.337471	-44.199938	41.280838	38.517470	-40.103981	1.156114e-06	-0.697011	0.000012	-0.002404	-1.099907	-0.003794
3	84.387738	-44.231544	41.223201	38.535332	-40.087436	1.537913e-06	-0.899827	0.000009	-0.002773	-1.419956	-0.004376
4	84.349040	-44.186206	41.272460	38.470772	-40.104916	7.895930e-07	0.722724	0.000008	0.001987	1.140529	0.003136
...	...	...	...	...	...	...	...	...	...	...	...
10344	84.335851	-44.187537	41.245811	38.501258	-40.092849	2.025278e-07	-0.464372	0.000005	-0.001006	-0.732745	-0.001588
10345	84.305829	-44.102650	41.208272	38.427926	-40.113957	9.244720e-06	1.646205	0.000017	0.006799	2.598176	0.010730
10346	84.369114	-44.220405	41.229959	38.525816	-40.083863	8.294915e-06	-0.707932	0.000083	-0.006440	-1.117100	-0.010162
10347	84.335274	-44.186430	41.250285	38.500882	-40.096101	4.584781e-07	-0.413323	0.000013	-0.001514	-0.652195	-0.002389
10348	84.329794	-44.179409	41.252718	38.479515	-40.096246	1.039107e-06	-0.895291	0.000006	-0.002279	-1.412723	-0.003597

Omnibus:	19289.464	Durbin-Watson:	1.980
Prob(Omnibus):	0.000	Jarque-Bera (JB):	149006747.820
Skew:	-13.366	Prob(JB):	0.00
Kurtosis:	590.232	Cond. No.	7.39e+03

	dfb_Intercept	dfb_weight	dfb_age	dfb_sex	dfb_hdresult	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	107.587851	-53.649882	34.262792	39.684384	-44.425101	7.323967e-08	-0.435534	0.000002	-0.000605	-0.729576	-0.001014
1	107.563791	-53.632728	34.264704	39.681722	-44.426264	1.102508e-06	-0.738549	0.000010	-0.002348	-1.237183	-0.003933
2	107.574437	-53.656463	34.312296	39.704613	-44.440307	2.067953e-06	-0.932201	0.000012	-0.003216	-1.561741	-0.005387
3	107.622629	-53.682803	34.243421	39.714215	-44.419825	1.218830e-06	-0.801060	0.000009	-0.002469	-1.341966	-0.004136
4	107.584728	-53.639306	34.287221	39.653970	-44.435241	4.426834e-07	0.541150	0.000008	0.001488	0.906572	0.002492
...	...	...	...	...	...	...	...	...	...	...	...
10344	107.572995	-53.640435	34.264858	39.680558	-44.424927	2.177197e-07	-0.481474	0.000005	-0.001043	-0.806532	-0.001748
10345	107.547430	-53.563905	34.229242	39.613932	-44.444114	7.099096e-06	1.442576	0.000017	0.005958	2.416956	0.009982
10346	107.602468	-53.669957	34.250755	39.703173	-44.416762	5.990370e-06	-0.601607	0.000083	-0.005473	-1.007797	-0.009168
10347	107.571176	-53.638959	34.269719	39.680823	-44.427920	5.800690e-07	-0.464911	0.000013	-0.001703	-0.778791	-0.002853
10348	107.562964	-53.630120	34.274800	39.657547	-44.428895	1.303771e-06	-1.002847	0.000006	-0.002553	-1.679941	-0.004277

	df	sum_sq	mean_sq	F	PR(>F)
hlthstat	5.0	5338.960006	1067.792001	45.13811	2.923497e-46
Residual	10343.0	244675.122883	23.656108	NaN	NaN

****intro****¶

Objectives¶

questions¶

Analysis¶

descrptive analysis¶

exploratory analysis¶

bmi model¶

transformation¶

Weight least squaren bmi model¶

transformation¶

logestic highbp model¶

bpsystol_model¶

weight¶

hct_model¶

transformation¶

weight¶

wtransformation¶

diabetes_logistic_model¶

ANOVA¶

intro¶